Stochastic Models of Severe Weather Watches and Warnings

            To alert the public to the possibility of a severe weather event — tornado (T), hail (H) with the diameter of at least ¾ of an inch, or convective wind (C) with the velocity of at least 50 knots — the National Weather Service (NWS) issues watches (V) and warnings (W).  The NWS Storm Prediction Center in Norman, Oklahoma, issues severe thunderstorm watches (SV), tornado watches (TV), and particularly dangerous situation watches (PV) for either thunderstorms or tornadoes.  The Weather Forecast Offices issue severe thunderstorm warnings (SW) and tornado warnings (TW).  Whereas the NWS verifies each product in terms of a probability of detection, a false alarm rate, and an average lead time, these performance measures do not provide information required for rational decision making under uncertainty.

            Two stochastic models are formulated that quantify the uncertainties in a manner required by decision models for optimal response:  (i) The one-stage model is for those whose response is triggered by a warning;  the decision tree has 15 terminal branches.  (ii)  The two-stage model is for those whose response process is triggered by a watch;  the decision tree has 63 terminal branches.  In each model, the sequences of different types of watches, warnings, events, and their complements, are identified and characterized by (i) chains of transition probabilities;  (ii) distribution functions of duration (of a watch type and a warning type), conditional on the alarm being either correct or false, distribution functions of lead time (of a watch type and a warning type), conditional on the alarm being correct, and (iii) distribution functions of area covered (by a watch type and a warning type), conditional on the alarm being correct or false.

            The challenge in modeling the sequences of watches, warnings, and events arises from the numerocity of their permutations and the non-exclusivity of their occurrences.  The objective, then, is to arrive at a parsimonious structure of the transitions, while extracting most predictive information from data records.  For example, the two types of warning (SW, TW) are not exclusive (because an area may be simultaneously under both warnings).  And it was discovered that a reinforced warning (RW), defined as TW preceded and overlapped (partly or totally) by SW, predicts tornadoes better than either TW or SW alone.  Moreover, RW and TW predict not only T, but also H and C with significant probabilities.  Thus to extract most information, it is best to put aside the NWS official nomenclature, and to treat watch and warning sequences as predictors for estimation of transition probabilities — as needed for making optimal decisions under uncertainty.